New solutions of the refraction integral

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Abstract
In a spherically symmetric inhomogeneous system, certain relations between refractive index and distance from the center of symmetry give closed solutions in elementary functions of the refraction integral. A careful formulation of the fundamental equations reveals that all such solutions reduce to special cases of one of eight standard forms, and that the theory of plane-parallel systems is mathematically identical. One special case gives a better representation of the Earth’s atmosphere than the traditionally used hypotheses of Cassini and Simpson.

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